The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

The probe technique is a simple mean to incorporate elastic and inelastic processes into quantum transport problems. Using numerical simulations, we demonstrate that this tool can be employed beyond the analytically tractable linear response regime, providing a stable solution for the probe parameters: temperature and chemical potential. Adopting four probes: dephasing, voltage, temperature, and voltage-temperature, mimicking different elastic and inelastic effects, we provide a systematic analysis of magnetic field and gate voltage symmetries of charge current and heat current in Aharonov-Bohm interferometers, potentially far from equilibrium. Considering electron current, we prove that in the linear response regime inelastic scattering processes do not break the Onsager symmetry. Beyond linear response, even (odd) conductance terms obey an odd (even) symmetry with the threading magnetic flux, as long as the system acquires a spatial inversion symmetry. When spatial asymmetry is introduced, particle-hole symmetry assures that nonlinear conductance terms maintain certain symmetries with respect to magnetic field and gate voltage. These analytic results are supported by numerical simulations. Analogous results are obtained for the electron heat current. Finally, we demonstrate that a double-dot Aharonov-Bohm interferometer can act as a charge rectifier when two conditions are met simultaneously: (i) many-body effects are included, here in the form of inelastic scattering; and (ii) time reversal symmetry is broken.